Discrete forms of Friedrichs' inequalities in the finite element method
Discrete maximum principle for interior penalty discontinuous Galerkin methods
A class of linear elliptic operators has an important qualitative property, the so-called maximum principle. In this paper we investigate how this property can be preserved on the discrete level when an interior penalty discontinuous Galerkin method is applied for the discretization of a 1D elliptic operator. We give mesh conditions for the symmetric and for the incomplete method that establish some connection between the mesh size and the penalty parameter. We then investigate the sharpness of...
Discrete Sobolev and Poincaré inequalities for piecewise polynomial functions.
Discrete Sobolev inequalities and error estimates for finite volume solutions of convection diffusion equations
The topic of this work is to obtain discrete Sobolev inequalities for piecewise constant functions, and to deduce error estimates on the approximate solutions of convection diffusion equations by finite volume schemes.
Discrete Sobolev inequalities and Lp error estimates for finite volume solutions of convection diffusion equations
The topic of this work is to obtain discrete Sobolev inequalities for piecewise constant functions, and to deduce Lp error estimates on the approximate solutions of convection diffusion equations by finite volume schemes.
Discrete Sobolev spaces and regularity of elliptic difference schemes
Discrete wavelet transforms accelerated sparse preconditioners for dense boundary element systems.
Discretization errors at free boundaries of the Grad-Schlüter-Shafranov equation.
Dispersive estimates and absence of embedded eigenvalues
In [2] Kenig, Ruiz and Sogge provedprovided , and is a second order operator with constant coefficients such that the second order coefficients are real and nonsingular. As a consequence of [3] we state local versions of this inequality for operators with coefficients. In this paper we show how to apply these local versions to the absence of embedded eigenvalues for potentials in and variants thereof.
Distortion analyticity for two-body Schrödinger operators
Distribution des résonances et décroissance de l’énergie locale pour le problème de transmission
Distributional asymptotic expansions of spectral functions and of the associated Green kernels.
Divergence boundary conditions for vector Helmholtz equations with divergence constraints
Divergence boundary conditions for vector Helmholtz equations with divergence constraints
The idea of replacing a divergence constraint by a divergence boundary condition is investigated. The connections between the formulations are considered in detail. It is shown that the most common methods of using divergence boundary conditions do not always work properly. Necessary and sufficient conditions for the equivalence of the formulations are given.
Divergence forms of the infinity-Laplacian.
The central theme running through our investigation is the infinity-Laplacian operator in the plane. Upon multiplication by a suitable function we express it in divergence form, this allows us to speak of weak infinity-harmonic function in W1,2. To every infinity-harmonic function u we associate its conjugate function v. We focus our attention to the first order Beltrami type equation for h= u + iv
Divergence stability in connection with the -version of the finite element method
Does Atkinson-Wilcox Expansion Converges for any Convex Domain?
2000 Mathematics Subject Classification: 35C10, 35C20, 35P25, 47A40, 58D30, 81U40.The Atkinson-Wilcox theorem claims that any scattered field in the exterior of a sphere can be expanded into a uniformly and absolutely convergent series in inverse powers of the radial variable and that once the leading coefficient of the expansion is known the full series can be recovered uniquely through a recurrence relation. The leading coefficient of the series is known as the scattering amplitude or the far...
Domain decomposition algorithms for first-order system least squares methods.
Domain decomposition and multigrid algorithms for elliptic problems on unstructured meshes.
Domain geometry and the Pohozaev identity.